What is the term for economics/capitalism that is fully based on Darwinian ideas?

There is no such economic system. It's not called Darwinian economics, because Darwinian theory of elimination of the unfit is that it's done by natural selection: the stronger take from the weaker by force and value is destroyed. By contrast, laissez-faire capitalism involves *voluntary exchange* of goods and services. Taking by the use of violence (robbery, theft) and fraud are illegal under capitalism. Instead, each party gives away what he values *less* in order to gain what he values more and thus both parties benefit, which is why societies get richer under a market system. Thus all analogies of capitalism with Darwinian evolution, on the basis of predation, battle, fighting, struggle for existence, power, and so on, are completely mistaken. For the same reason, it is mistaken to talk about the "power" of market actors, big corporations, and so on. Market actors do not have power, because they cannot force anyone into any transaction. They exist only because of the actions of millions of people in voluntarily handing over their wealth in order to get whatever the seller is selling. However it is true that, under a system of free market capitalism, people who provide what the great mass of people want, will tend to make profit, and those businesses who do not provide what they want, will tend to make losses and eventually go broke and return to the ranks of wage-earners. However there is nothing immoral, unfair, or zero-sum about this process. It is the process by which all of use engage in *peaceful* co-operation to use natural resources to satisfy human wants, more and better than any other system has ever done. The system that is based on Darwinian ideas is *government*. The state is the group in society exercising a legal monopoly of the use of force. It is by definition the most violent and aggressive party because it claims are right of unilateral unprovoked aggression. It's entire modus operandi is based on getting what it wants, by taking as much of the life, property or liberty as it wants from any of its subjects, by force or threats of force. That's the *real* law-of-the-jungle, dog-eat-dog, Darwinian ethos - the state.

Darwinism is a poor choice for an economic term Evolution works on the species over a long period NOT on individuals it "rewards" what woks for species, not the individual Capitalism" for example is just a system that has advantages and disadvantages economics is VERY dependent on opinion. Read some Robert Reich or Richard Wolff and certainly read "Das Kapital" ( in translation form the german if necessary)